MMW midterms (ril)

Inductive Reasoning

is the process of reaching a general conclusion by examining specific examples

Conjecture

it is the conclusion formed

Galileo Galilei

he used inductive reasoning to discover that the time required for a pendulum to complete a one swing, depend on the length of a pendulum

Deductive Reasoning

is the process of reaching a conclusion by applying general assumptions, procedures, or principles

Logic Puzzles

can be solved by using deductive reasoning and a chart that enables us to display the given information in a visual manner

Example of inductive reasoning

During the past 10 years, a tree has produced plums every other year. Last year, the tree did not produce any, so this year it will produce plums

Example of deductive reasoning

All home improvements cost more than the estimate. The contractor estimated that my home improvement will cost ₱35,000. Thus, my home improvement will cost more than ₱35,000.

George Polya

one of the foremost recent mathematicians to make a study about problem solving. He was born in hungary and moved to united states in 1940

Understand the problem'; Devise a plan; Carry out the plan; Review the solution

Polya’s four-step problem solving strategy

Understand the Problem

This part of Polya’s problem solving strategy is often overlooked. You must have a clear understanding about the problem.

Devise a plan

these are the variety of techniques to solve a problem

Carry out the plan

once you have devised a plan, you must carry it out

Sequence

it is an ordered list of numbers

Terms of the Sequence

the numbers in a sequence separated by commas

𝑎1

represents the first term of a sequence

𝑎2

represents the second term of a sequence.

𝑎3

represent the third term of a sequence.

𝑎𝑛

represents the nth term of a sequence.

nth term

is a formula with n in it which enables you to find any terms of a sequence without to go up from one term to the next

n

stands for the term number

dn + (a-d)

formula of nth term

d

difference between the terms

a

is the first term

Difference table

shows the differences between the successive terms of the sequence

First differences

these are the differences in row 1

Second differences

these are the differences of the first differences

Third differences

these are the differences in the second differences